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A rectangular flat sheet of metal is to be converted into an open box

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gmatcruiser
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A rectangular flat sheet of metal is to be converted into an open box [#permalink] New post   31 Jan 2015, 09:21
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A rectangular flat sheet of metal is to be converted into an open box. To do this, four squares with sides x must be cut off.
What value of x would yield a box with the greatest volume?

1. 5
2. 4
3. 3
4. 2
5. 1
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sterling19
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Re: A rectangular flat sheet of metal is to be converted into an open box [#permalink] New post   01 Feb 2015, 19:29
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I'm looking for a shortcut here; feel free to correct me.

\(V = l*w*h\)
so\(V = x*(15-2x)*(12-2x)\)

\(A = 5*5*2 = 5^2 * 2 = 25*2\)
\(B = 4*7*4 = 2^4 *7 = 16*7\)
\(C = 3*9*6 = 3^4 *2 = 81*2\)
\(D = 2*11*8 = 2^4 *11 = 16*11\)
\(E = 1*13*10 = 130\)

From this we can see that D must be larger than B and C must be larger than A.
Finish multiplying C and D to get 162 and 176, respectfully. D is the correct answer.
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susheelh
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Re: A rectangular flat sheet of metal is to be converted into an open box [#permalink] New post   04 May 2017, 22:12
Hi!

This seems to be an interesting question. The Only way to solve this seems to be by testing the answer choices. It would be a good question to save it for later practice. However, I dont see the usual "Add to PDF" link for this question. Can Someone help me how to do this? Bunuel or others - your thoughts please. Both on how to solve and how to "Add to PDF"?
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grassmonkey
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Re: A rectangular flat sheet of metal is to be converted into an open box [#permalink] New post   26 Aug 2017, 22:19
Best practices for something like this is to test the extreme values in the answer choices first (1 and 5), whichever one is bigger test the next largest one and the proceed in descending order until you're either satisfied or you need to bail.

I'd be interested to hear if the experts on here have a better way to solve this than sterling19's method.

GMAT questions usually try and get at some conceptual point. This question really just seems to be testing whether you can punch in answer choices and see which one gives you the biggest number.
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gmatclubot
Re: A rectangular flat sheet of metal is to be converted into an open box [#permalink]
26 Aug 2017, 22:19

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